Encyclopedia of Microtonal Music Theory

thirteenth / 13th / diatonic-13th

[Joe Monzo]

A diatonic interval which traverses 12 steps in a diatonic scale, and covers a pitch distance bounded by 13 nominals inclusively, an octave plus a 6th. This refers to the generic usage of "13th" without a qualifying adjective, which often precedes the interval name in standard diatonic usage. Thus, the various different types of diatonic 13ths are (in order of size from smallest to largest):

diminished-13th

minor-13th

major-13th

augmented-13th

The 13th is the largest interval normally recognized by name in traditional harmony, since the method of building a chord in 3rds results in the double-octave (15th) when going beyond this, and thus returns to the root chord-member.

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